magepker728

2 years ago

How would you transform the graph of y= f (x ) to obtain the graph of y= -3f (x- 2) +5 ? If (7, -3) is a point on the graph of y= f (x ) , what would be the corresponding point on the graph of y=-3f (x- 2)+ 5 ?

There are three aspects to the transformation.
Think first about that "-3" in front of the f(x-2)... and just think for a minute as if was just -3f(x). So if that was the only transformation, it would take the original function f(x), and it would make it 3 times larger for every x input, but it would also flip it... so any negative values in f(x) would become positive (and 3 times larger) in -3f(x).

Next, think about what the (x-2) does as the function input in comparison to the original function, f(x).
f(x) gives some value for any input x.
f(x-2) will take values for x that are 2 larger and then return the same f.
In other words, say f(x) = 10 when x=0... f(0) = 10
Then in the transformed function f(x-2), it will also be equal 10, but it will shift over to be equal 10 when x = 2.
So f(x-2) is a transformation that shifts the function right by 2 units compared with f(x)

So, with those two parts of the transformation, you can say that -3f(x-2) transforms f(x) by making it 3 times larger, flipping it across the x-axis, and shifting it all right by 2 units.
The last transformation adds 5 to everything else. Can you see what shift will occur as a result?

1)shift the function to the right by 2 points,
2) flip the graph down, around x axis.
3) Re- calibrate y axis in such a way that 3 units in the previous graph is 1 unit in the present graph
4) Shift the resulting graph up by 5 points